Finite Element Simulation of Interfacial Flows on Unstructured Meshes using a Second-order Accurate VOF Method

This thesis consists of two major parts. In the first part a two-dimensional numerical model of interfacial flow phenomena has been developed, consisting of a finite element discretization of the time-dependent Navier-Stokes equations for immiscible, Newtonian, laminar, isothermal incompressible flows, with a volume-of-fluid (VOF) technique for interface capturing. A new formulation of the pressure Poisson equation that requires the discretization of a second-order derivative is used for the flow field on a fixed Eulerian grid. This approach enables us, in particular, to implement equal-order interpolation for the velocity and pressure. Streamline upwind Petrov-Galerkin (SUPG) stabilization is used for convection-dominated flows. Fluid interfaces are reconstructed and advected using a second-order accurate VOF method. An accurate least-squares circle-fit technique has been developed for curvature calculation on triangular meshes, and then used to implement surface tension forces on a single layer of interface elements. A dynamic contact angle model is implemented based on the Kistler correlation, that serves as a means to evaluate the dynamic contact angle as a function of grid-spacing and the contact-line velocity. Two-fluid flows with density ratios ranging from 10 to 106 are simulated, and the performance of the model is evaluated via the static-drop test case and several examples of bubble dynamics. Finally, the model is applied to the coalescence of two bubbles, the merging of a bubble into a free surface, and the impact of a glycerin droplet onto horizontal wax and glass surfaces, and yields good agreement with experimental measurements and other numerical results. In the second part, a second-order accurate three-dimensional VOF method for unstructured tetrahedral meshes has been developed. The method approximates interface geometries as piecewise planar, and advects volume via a forward trajectory remapping method. Two different methods are used to calculate the interface normal: a differential least-squares (DLS) method that is first-order accurate, and a geometric least-squares (GLS) method that is second-order accurate. Second-order accuracy of the VOF algorithm is demonstrated for simple translations and rotations as well as vigorous threedimensional vortex deformation.

Department dc:contributor.department

Mechanical and Industrial Engineering

Year dc:date.issued

2014

Author dc:creator

• Sultana, Zakia

Advisors dc:contributor.advisor

• Mostaghimi, Javad
• Paraschivoiu, Marius

• FEM
• Interfacial flow
• VOF

Language dc:language.iso

en_ca

Handle dc:identifier.uri

http://hdl.handle.net/1807/67314

OAI identifier oai:identifier

oai:utoronto.scholaris.ca:1807/67314